Omega Results for The Divisor and Circle Problems Using The Resonance Method

2025/04/23 by Kamalakshya Mahatab, Mahatab, Kamalakshya · 2 citations
Mathematics · #11M06 #11N37 #11P21 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.17032

openalex publication_date 2025/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the resonance method to obtain large values of general exponential sums with positive coefficients. As applications, we show improved Ω-bounds for Dirichlet and Piltz divisor problems, Gauss circle Problem, and error term for the mean square of the Riemann zeta function and the Dirichlet L-function.

Cited by

• Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
• The Piltz divisor Problem in Number Fields Using The Resonance Method

Related

• An additive application of the resonance method
• Resonances and Ω-results for Exponential Sums Related to Maass Forms for SL(n,\mathbb Z)
• Omega results for the divisor and circle problems
• The Piltz divisor Problem in Number Fields Using The Resonance Method
• Note on the resonance method for the Riemann zeta function